Is there a problem talking while washing your hand for netilas Yadayim?
While washing, it is permitted to speak. After one has completed the washing, and before one makes the blessing of al netilas yadayim, one should be careful not to speak.
The obligation to make a blessing in only incumbent after one has completed washing one’s hands, and therefore there would be no problem in speaking until one finishes washing. After washing, some write that it is forbidden to speak (see Tzelach, derush 4, no. 22; Shevet Halevi, vol. 3, no. 12), whereas others are less stringent, because the washing itself is not complete until one’s hands are dry (see Eliyah Rabba 162:1; Rivevos Efraim 1:128 (quoting from R. Porat); Maharam Brisk (3:39, sec. 5, quoting from Daas Kedoshim 166); Oneg Yom Tov (18), quoting from Shulchan Aruch Harav. See, at length, Yabia Omer, vol. 8, no. 26, sec. 6.